直觉模糊信息集成理论及应用(英文版)

    书籍
    数学书籍
Intuitionistic Fuzzy Information Aggregation: Theory and Applications, the first book to provide a thorough and systematic introduction to the intuitionistic fuzzy aggregation methods, the correlation, distance and similarity measures of intuitionistic fuzzy sets, and various decision-making models and approaches based on the above-mentioned information processing tools. Through numerous practical examples and illustrations with tables and figures, it offers researchers and professionals in the field of fuzzy mathematics, information fusion and decision analysis, the most recent research findings developed by the authors.

Zeshui Xu is Professor at the PLA University of Science and Techology, China.
Xiaoqiang Cai is Professor at the Chinese University of Hong Kong, China.

《直觉模糊信息集成理论及应用(英文版)》
Chapter 1 Intuitionistic Fuzzy Information Aggregation
1.1 Intuitionistic Fuzzy Sets
1.2 Operational Laws of Intuitionistic Fuzzy Numbers
1.3 Intuitionistic Fuzzy Aggregation Operators
1.4 Intuitionistic Fuzzy Bonferroni Means
1.5 Generalized Intuitionistic Fuzzy Aggregation Operators
1.6 Intuitionistic Fuzzy Aggregation Operators Based on Choquet Integral
1.7 Induced Generalized Intuitionistic Fuzzy Aggregation Operators
References
Chapter 2 Interval-Valued Intuitionistic Fuzzy Information Aggregation
2.1 Interval-Valued Intuitionistic Fuzzy Sets
2.2 Operational Laws of Interval-Valued Intuitionistic Fuzzy Numbers
2.3 Interval-Valued Intuitionistic Fuzzy Aggregation Operators
2.4 Interval-Valued Intuitionistic Fuzzy Bonferroni Means
2.5 Generalized Interval-Valued Intuitionistic Fuzzy Aggregation Operators
2.6 Interval-Valued Intuitionistic Fuzzy Aggregation Operators Based on Choquet Integral
2.7 Induced Generalized Interval-Valued Intuitionistic Fuzzy Aggregation Operators
References
Chapter 3 Correlation, Distance and Similarity Measures of Intuitionistic Fuzzy Sets

　　Since it was introduced by Zadeh in 1965, the fuzzy set theory has been widely applied in various fields of modern society. Central to the fuzzy set is the extension of the characteristic function taking the value of 0 or 1 to the membership function which can take any value from the closed interval [0,1]. However, the membership function is only a single-valued function, which cannot be used to express the evidences of sup-port and objection simultaneously in many practical situations. In the processes of cognition of things, people may not possess a sufficient level of knowledge of the prob-lem domain, due to the increasing complexity of the socio-economic environments. In such cases, they usually have some uncertainty in providing their preferences over the objects considered, which makes the results of cognitive performance exhibit the char-acteristics of affirmation, negation, and hesitation. For example, in a voting event, in addition to support and objection, there is usually abstention which indicates hesita-tion and indeterminacy of the voter to the object. As the fuzzy set cannot be used to completely express all the information in such a problem, it faces a variety of limits in actual applications.
　　Atanassov (1983) extends the fuzzy set characterized by a membership function to the intuitionistic fuzzy set (IFS), which is characterized by a membership function, a non-membership function and a hesitancy function. As a result, the IFS can describe the fuzzy characters of things more detailedly and comprehensively, which is found to be more effective in dealing with vagueness and uncertainty. Over the last few decades, the IFS theory has been receiving more and more attention from researchers and practitioners, and has been applied to various fields, including decision making,logic programming, medical diagnosis, pattern recognition, robotic systems, fuzzy topology, machine learning and market prediction, etc.
　　The IFS theory is undergoing continuous in-depth study as well as continuous expansion of the scope of its applications. As such, it has been found that effective aggregation and processing of intuitionistic fuzzy information becomes increasingly important. Information processing tools, including aggregation techniques for intu-itionistic fuzzy information, association measures, distance measures and similarity measures for IFSs, have broad prospects for actual applications, but pose many in-teresting yet challenging topics for research.
　　In this book, we will give a thorough and systematic introduction to the latest research results in intuitionistic fuzzy information aggregation theory and its ap-plications to various fields such as decision making, medical diagnosis and pattern recognition, etc. The book is organized as follows:
　　Chapter 1 introduces the aggregation techniques for intuitionistic fuzzy informa-tion. We first define the concept of intuitionistie fuzzy number (IFN), and based on score function and accuracy function, give a ranking method for IFNs. We then define the operational laws of IFNs, and introduce a series of operators for aggregat-ing intuitionistic fuzzy information. These include the intuitionistic fuzzy averaging operator, intuitionistic fuzzy bonferroni means, and intuitionistic fuzzy aggregation operators based on Choquet integral, to name just a few. The desirable properties of these operators are described in detail, and their applications to multi-attribute decision making are also discussed.
　　Chapter 2 mainly introduces the aggregation techniques for interval-valued intu-itionistic fuzzy information. We first define the concept of interval-valued intuitionis-tic fuzzy number (IVIFN), and introduce some basic operational laws of IVIFNs. We then define the concepts of score function and accuracy function of IVIFNs, based on which a simple method for ranking IVIFNs is presented. We also introduce a number of operators for aggregating interval-valued intuitionistic fuzzy information, including the interval-valued intuitionistic fuzzy averaging operator, the interval-valued intu-itionistic fuzzy geometric operator, the interval-valued intuitionistic fuzzy aggregation operators based on Choquet integral, and many others. The interval-valued intuition-istic fuzzy aggregation operators are applied to the field of decision making, and some approaches to multi-attribute decision making based on interval-valued intuitionistic fuzzy information are developed.
　　Chapter 3 introduces three types of measures: association measures, distance measures, and similarity measures for IFSs and interval-valued intuitionistic fuzzy sets (IVIFSs).
　　Chapter 4 introduces decision making approaches based on intuitionistic prefer-ence relation. We first define preference relations, then introduce the concepts of interval-valued intuitionistic fuzzy positive and negative ideal points. We also utilize aggregation tools to establish models for multi-attribute decision making. Approaches to multi-attribute decision making in interval-valued intuitionistic fuzzy environments are also developed. Finally, consistency analysis on group decision making with intu-itionistic preference relations is given.
　　Chapter 5 introduces multi-attribute decision making with IFN/IVIFN attribute values and known or unknown attribute weights. We introduce the concepts such as relative intuitionistic fuzzy ideal solution, relative uncertain intuitionistie fuzzy ideal solution, modules of IFNs and IVIFNs, etc. We then establish projection models to measure the similarity degree between each alternative and the relative intuitionistic fuzzy ideal solution and the similarity degree between each alternative and the relative uncertain intuitionistic fuzzy ideal solution, by which the best alternative can be obtained.
　　Chapter 6 introduces aggregation techniques for dynamic intuitionistic fuzzy infor-mation and methods for weighting time series. We introduce the concepts of intuition-istic fuzzy variable and uncertain intuitionistic fuzzy variable. We describe dynamic intuitionistic averaging operators, based on which dynamic intuitionistic fuzzy multi-attribute decision making and uncertain dynamic intuitionistie fuzzy multi-attribute decision making problems are tackled.
　　Chapter 7 considers multi-attribute group decision making problems in which the attribute values provided by experts are expressed in IFNs, and the weight informa-tion about both the experts and the attributes is to be determined. We introduce two nonlinear optimization models, from which exact formulas can be obtained to derive the weights of experts. To facilitate group consensus, we introduce a nonlin-ear optimization model based on individual intuitionistic fuzzy decision matrices. A simple procedure is used to rank the alternatives. The results are also extended to interval-valued intuitionistic fuzzy situations.
　　This book is suitable for practitioners and researchers working in the fields of fuzzy mathematics, operations research, information science and management science and engineering, etc. It can also be used as a textbook for postgraduate and senior-year undergraduate students.
　　This work was supported by the National Science Fund for Distinguished Young Scholars of China under Grant 70625005.
　　Zeshui Xu, Xiaoqiang Cai
　　Hong Kong
　　September, 2011